Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier-Stokes Equations

被引：22

作者：

Han, Weimin ^{[1
]}

Czuprynski, Kenneth ^{[2
]}

Jing, Feifei ^{[3
,4
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Univ Iowa, Program Appl Math & Computat Sci AMCS, Iowa City, IA 52242 USA

[3] Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China

[4] Northwestern Polytech Univ, Xian Key Lab Sci Computat & Appl Stat, Xian 710129, Shaanxi, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2021年 / 89卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Navier-Stokes equations; Hemivariational inequality; Existence; Uniqueness; Mixed finite element method; Error estimation; SLIP BOUNDARY-CONDITIONS; NUMERICAL-ANALYSIS; LEAK;

D O I：

10.1007/s10915-021-01614-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop and study the mixed finite element method for a hemivariational inequality of the stationary Navier-Stokes equations (NS hemivariational inequality). The NS hemivariational inequality models the motion of a viscous incompressible fluid in a bounded domain, subject to a nonsmooth and nonconvex slip boundary condition. The incompressibility contraint is treated through a mixed formulation. Solution existence and uniqueness are explored. The mixed finite element method is applied to solve the NS hemivariational inequality and error estimates are derived. Numerical results are reported on the use of the P1b/P1 pair, illustrating the optimal convergence order predicted by the error analysis.

引用

页数：22

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